Sounds like your windscreen wiper motor is being overloaded in some way and the thermal cutout is cutting the power to stop the motor from burning out. If you continue to use it as it is it will burn out the motor and they are expensive.
The most common cause of motor overload is when the sliding mechanism under the "turtle shell"cover of the wiper gearbox becomes dry and needs regreased. Initially, lift the cover at the base of the wiper arm and grease the pushrod that protrudes from the wiper drive , this is best done when the wiper arm is at full extension using the ignition switch to stop the wiper at this point. Use silicon or waterproof grease if available and coat as much of the pushrod as possible.
If this does not help you need to remove the "turtle shell "cover and,depending on your model that can be easy or a problem. Try greasing the pushrod first and let me know how that goes.
Geo.